Diagnosis
You've got a partial clog in the water line or the dispenser itself. The most common spot is the filter, if it's old, or the inlet screen right where the water line connects to the fridge.
How to Fix It
Start with the simplest. 1) Replace the water filter. Twist the old one out, pop the new one in. Run a couple gallons of water through the dispenser to clear air and check flow. If it's still slow, 2) check the inlet screen. Shut off the water supply at the valve behind the fridge. Disconnect the water line where it meets the fridge (have a towel ready). You'll see a tiny plastic screen in the fridge's inlet valve. Use needle-nose pliers to gently pull it out and rinse it under water to clear any sediment.
If That Didn't Work
The water inlet valve itself could be failing and not opening fully. It's a less common fix, but if the screen was clean and the filter new, it's the next suspect.
Heads Up
Always shut off the water supply before disconnecting any lines. And when you run water after changing the filter or clearing a clog, expect some sputtering and air pockets for the first minute or two – that's normal.